Digging Deeper into … 3-D Objects

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Digging Deeper into … 3-D Objects

The first obvious question to be addressed is why this topic is called 3-D objects in Operation Maths, when most other textbooks, and even the curriculum refer to this topic as 3-D shapes?

In the PDST Shape and Space manual, it is suggested that “using the word ‘shape’ to describe 2-D shapes and 3-D shapes can cause confusion for pupils”. For example, asking pupils to ‘describe the shape of this shape’ highlights one problem. Another problem is that pupils must be able to think of all cuboids as being ‘the same shape’, while mathematically speaking all cuboids are not the same shape.

The manual goes on to suggest that it would be more helpful to refer to 3-D things as ‘objects’. Using ‘objects’ also reinforces the notion that if it can be physically handled/picked up, it must be a 3-D object, as opposed to a 2-D shape which should always only have length and width, not depth/height.

So, throughout the Operation Maths books, this topic is called 3-D objects to avoid confusion and to provide clarity for the pupils. However, wherever there is reference to “strand unit”, the term 3-D shapes is used, as this is the term used in the curriculum.

CPA

As usual, this topic is explored using a CPA approach, where the initial focus is on the exploration of 3-D objects and the identification of similarly shapes objects from the child’s environments. And, in a similar way to the teaching of 2D shapes, while the 3-D objects will be identified by name, the greater focus should be on their properties, as appropriate to each class level e.g.

identifying whether the objects roll, stack, or slide

relating the properties of each object to its purpose and use in the environment

recording, sorting and comparing according to the number and shape of faces and curved surfaces

recording, sorting and comparing according to the number of edges and vertices (corners)

It is important that the children discover the properties of the 3-D objects by hands-on investigations and by classifying and sorting. Sorting activities help develop the children’s communication, observation, reasoning and categorising skills, and thus will help to develop a conceptual understanding of the objects. In the senior classes using online interactive sorting activities based on Venn diagrams or Carroll diagrams can be very useful. Asking children to bring in examples of 3-D objects from home will help them to become aware of 3-D objects in their environment.

Faces, curved surfaces and edges

How many faces on a cylinder? Three or two?

Traditionally, in Ireland, and in Irish textbooks, a cylinder was recorded as having three faces. However, this is not mathematically correct, as strictly speaking a face is flat, and a 2D shape (figure), so therefore a cylinder has in fact only two faces, (both circles), and one curved surface. And while some may argue that a cylinder has a third face i.e. the rectangular shape you see when you disassemble the net of the 3-D object, in this disassembled state it is no longer a cylinder, since it can no longer roll, a specific property of all cylinders.

Another way to think about the faces of 3-D objects is to consider the number and shape of the resulting outlines of tracing around each surface of the 3-D object. It is only possible to trace around the opposite ends/bases of the cylinder, since only these are flat, thus it has only two faces, both of which are circular in shape. Similarly, it is only possible to trace around one surface on a cone, which therefore means it has only one face (a circle) and one curved surface.

And how many edges on a cylinder? Officially none, as an edge is where two flat faces meet and the faces on a cylinder are on opposite sides and do not touch/meet. However, that leaves the problem of how to describe the place where each face meets the curved surface. So in Operation Maths, as occurs typically in other primary texts in other countries, there is a distinction made between straight edges (which are in fact true edges) and curved edges (which strictly speaking are not edges).

In 5th and 6th class, it is important that the children realise that only some of the 3D objects are also polyhedra, and that only five of these are categorised as platonic solids.

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